Chevron Corp. has begun requiring some employees to receive Covid-19 vaccinations and is evaluating mandates throughout its entire workforce as the oil-and-gas industry contends with rising infections, according to people familiar with the matter.

The second-largest U.S. oil company is one of the first major oil-and-gas producers to implement such requirements as the industry wrestles with unvaccinated field workers. Outbreaks of the virus have recently been affecting operations in key sites such as the offshore platforms of the Gulf of Mexico and the Permian Basin of Texas and New Mexico, several industry executives said.

Chevron is now requiring expatriate employees, workers traveling internationally, and employees on U.S.-flagged ships to receive vaccinations, said company spokesman Braden Reddall. It will also require offshore workers in the Gulf of Mexico and some onshore support staff to be vaccinated by Nov. 1, he said. The requirements cover thousands of employees.

A Hess oil platform near the Gulf Coast. The oil producer is requiring some employees to be vaccinated.

Photo: Eddie Seal/Bloomberg News

“Chevron is committed to protecting the health of our people, and vaccinations are the strongest safeguard against this virus,” Mr. Reddall said.

Executives at the San Ramon, Calif.-based company are also evaluating the feasibility of mandates for each Chevron business unit and could implement such requirements more broadly through its roughly 47,000-member workforce, people familiar with the matter said.

The analysis includes the risk of infection within the unit and the availability of vaccines within the dozens of countries in which Chevron operates, the people said, adding that there is currently no plan for a companywide mandate. Chevron plans to allow exceptions to some employees for health or religious reasons, Mr. Reddall said.

Covid-19’s Delta variant is proliferating world-wide threatening unvaccinated populations and economic recovery. WSJ breaks down events in key countries to explain why Delta spreads faster than previously detected strains. Composite: Sharon Shi The Wall Street Journal Interactive Edition

Other oil-and-gas companies are considering similar policies, say people familiar with the matter. Oil producer Hess Corp. is requiring some employees to be vaccinated and refiner Valero Energy Corp. has implemented a requirement for new hires, say people familiar with the plans.

Hess has told its offshore workers in the Gulf of Mexico they must be vaccinated by Nov. 1 after an outbreak on one of its platforms there in recent weeks, according to a person familiar with the matter.

“Given the highly infectious nature of the Delta variant and the rising number of Covid-19 cases in the U.S., we are implementing additional preventative measures in our Gulf of Mexico operations to help ensure safety and business continuity,” said Hess spokeswoman Lorrie Hecker.

A Phillips 66 refinery in Rodeo, Calif. The refiner said it won’t require its employees to receive vaccinations.

Photo: David Paul Morris/Bloomberg News

Not everyone in the industry supports company vaccination mandates. Phillips 66, one of the largest U.S. refiners, won’t require its employees to receive vaccinations, according to Chief Executive Greg Garland.

“We strongly encourage people to be vaccinated,” Mr. Garland said. “But we haven’t yet crossed a bridge where we’re going to say everyone needs to be vaccinated.”

Mr. Garland said the company has offered vaccinations on-site at some of its refineries and believes more than 80% of the employees at its Houston headquarters are vaccinated. The company recently reinstituted masking and social-distancing policies it previously had in place but dropped earlier this year.

Industry executives say they face a divide within their workforce over vaccines. Among primarily white-collar office employees, vaccination rates are high, the executives say. But field employees who work the industry’s refineries, chemical plants, offshore platforms and other critical operations have much lower vaccination rates, internal company surveys show.

Similar workforce divides over vaccinations are bedeviling the broader corporate world. They are especially stark in industries, such as energy, where some workers can work from home and others can’t and where views on vaccines differ widely. The energy industry produces fuels and chemicals essential to the global economy that require round-the-clock operations staffed by employees working in proximity to one another.

A significant number of workers have been infected in the Permian Basin, the most productive U.S. oil field, putting stress on an already thin workforce there, according to the executives. The same is true among workers in Louisiana, sparking concerns over outbreaks on remote offshore platforms where employees live for weeks at a time during shifts, some of the executives said.

The industry’s largest employers, oil-field service companies—which operate drilling rigs, fracking units and other equipment—have experienced a rash of Covid-19 cases among vaccine-hesitant workers in recent weeks, say analysts and industry executives.

“ ‘I have employees fighting for their lives right now.’ ”

— Ann Fox, chief executive of Nine Energy Service

“You are dealing with a population that largely does not believe in vaccination,” said Ann Fox, the chief executive of Nine Energy Service Inc., a company that helps complete oil wells and provides other services. “I have employees fighting for their lives right now.”

Ms. Fox said the Delta variant has strained the service workforce, which was already thin after many workers left the industry last year following the collapse of commodity prices. She would like to implement a vaccine requirement for employees, but believes she would be unable to attract enough workers.

Ms. Fox fears that the thin workforce could affect U.S. oil production next year if current conditions continue. Many oil producers will have to drill new wells to maintain production levels, and could find it difficult to find roughnecks to staff drilling rigs, she said.

She said she hopes that oil-and-gas producers, her customers, will require vaccinations that could help establish an industrywide standard that vaccines are required for employment.

“It’s a very fine line to walk as a business leader,” Ms. Fox said. “Nobody wants to be the first mover.”

Write to Christopher M. Matthews at christopher.matthews@wsj.com